An incarnation of multi-field cosmology is the so called chiral-cosmology [1]}, in which the scalar fields define an “internal space” with a certain metric component \(m_{ab}\) . They also interact in a non-standard manner within their kinetic terms, their couplings are governed by the metric \(m_{ab}\)  (in short, we will replace \(\delta ^{ab}\rightarrow m^{ab}\)  in (REF )). This metric can be seen as arising from casting a non-minimally coupled multi-scalar-tensor theory as General Relativity (i.e., in going from the Jordan frame to the Einstein frame) [2]}. Non-minimal couplings are indeed required when considering the quantization of scalar fields in curved backgrounds [3]}, the use of non-canonical fields in (effective) descriptions of the early universe in Einstein's general relativity is therefore theoretically consistent with standard quantum field theory.
